Hi there,
hope that this comes not too late!
LB refers to Luciano Bertoni medium (I'm not shure about the name but you can
look after it for example in the Current Protocols for Mol Biol Ausubel et al,
which is really better than the Maniatis).
We usually take for all protein expressions the TBY medium which has good
results (10g yeast, 10g tryptone 5g NaCl). If the overexpression is not working
with this medium there is something wrong with your cloning or with your
expression product that might be lethal for the coli cells.
regards
Kai